What always puzzled me was why there are so many stable orbits in our universe. For example, the Earth has been spinning around the Sun for billions of years without falling into the Sun or flying into outer space. Wouldn't any stable orbit require a perfect balance of forces? Shouldn't a stable orbit be as uncommon as a needle that is balanced on its tip? Also, even though the mechanics are different, what force prevents orbiting electrons from falling into the nucleus, or from flying out of the atom? Are the electrostatic force and inertial force the only forces resposible for the electrons stable orbit? Other forces seem to be responsible since electrons are only found at specific distances from the nucleus of the atom, but I'm only aware of the four fundamental interactions. Aren't orbitals proof that there must be other forces present in the atom?
That is a really interesting question. My quantum mechanics is too shaky to really answer the electron question, other than to say that for the electron it probably has something to do with wave functions. My classical physics is good enough to talk about the orbit question. In most orbits there is not a perfect balance of forces and the satellite actually changes speed during the course of an orbit. In fact, if you start at any given point with any given velocity there are only two ways to not have a stable orbit in classical physics. One is to have a an orbit that intersects the primary (the satellite crashes) and the other is to have a satellite with greater than escape velocity (the satellite just leaves). All other initial conditions result in a stable orbit. In books that talk about string theory and how several dimensions are "curled up" they often mention that a universe with 4 spatial dimensions would have unstable orbits. And apparently 2 spatial dimensions would somehow lead to no gravitational formation of planets or stars. I don't know the math behind that, but I guess that in order for us to exist the universe must be 3D specifically in order for stable orbits to exist. "I think therefore the stars are" Please Register or Log in to view the hidden image! -Dale
Dale, There is only one condition that can result in a stable orbit : if the inertial force of the satellite pushing away from the mass is equal to the force of the gravitational attraction between the object and the mass. Even the slightest difference between these two forces would result in a "chain reaction" that would either cause the satellite to crash into the mass or to fly off. And yet, the Earth, and the other planets in our solar system, have somehow managed to orbit the Sun for billions of years without this happening. I wouldn't believe it if I didn't know it was true. It just seems that there should be far fewer perfect orbits in the universe than there actually are.
What do you mean? There is no such thing as an "inertial force". There is no repulsive force of any kind involved in an orbit and therefore nothing to balance. -Dale
Dale, All moving masses have inertia. If you attempt to change the direction or speed of a moving mass, you will notice that there is a force that is trying to keep the mass moving at a constant speed and in a straight line. This is what I'm referring to when I say "inertial force".
Just remember: because of conservation of angular momentum, as the planets get closer to the sun, their velocities increase. If the velocity increases so does the "inertial force" or centrifugal force (if we look in the non-inertial reference frame. So really it is not that incredible, the planets just need to get close enough so that the two forces are near equal; there are fluctuations however, since every orbit is not a circle (though many are quite close). The question I want to know is why all the planets orbit the sun on very close to the same plane? What are the explanations for that?
You're still anchored in the past if you think that an electron around an atom follows an orbit like a planet around a star. Bohr's model was that way, but in modern Quantum mechanics, electrons are a sort of cloud of probability, so they don't follow a definite orbit.
Even stationary mass has inertia. Newton's F == m a is the statement governing inertia. There is no such force as you describe. If you apply a force to any object it will accelerate according to F == m a. The idea of inertia is simply that if F == 0 then a == 0 and therefore the object moves at a constant velocity. If F != 0 then the object will accelerate according to F == m a. There is no opposing "inertial force" involved. Try drawing a free-body diagram for a satellite. You will see that there is only one force, the gravitational force (aka weight). A body in orbit is therefore constantly accelerating; it is not in a static state where forces are balanced. If it were experiencing balanced forces as you suggest then it would not orbit at all; its motion would be a straight line instead of an ellipse. Unbalanced forces are required for orbital motion. -Dale
Prosoothus, It is the attractive and repulsive aspects of magnetism that keeps things on their orbits. All particles are small magnets with two poles, so the earth is also a great magnet, since it is composed of atomic particles. I said this to you 7 months and 3 days ago, did you already forget it? The rotation of the earth ("caused" by the magnetic forces) generates "gravity".
Orbits only LOOK stable to our macroscopic view. The gravity of the sun, every planet, every satelite, every asteroid, the Oort cloud and, in fact every gravitational object in the universe is constantly mutually interacting. Thus every moment every orbit is changed to some extent from its previous orbit. Apparently, in most cases on record, these deviations are small enough to not be catastrophic or even be easily noticeable. But they are there. I am not engaging in a debate on this, but, just how much evidence DO we have that our solar system orbits have not recognizeably changed for billions of years? Perhaps not as much evidence as we might faithfuly hope to be there. Please Register or Log in to view the hidden image! BTW, in a two body system in which one body were so comparatively small that its mass were negligeable, such as a grain of sand orbiting the sun, the orbit could virtually be perfectly circular and would have a constant velocity. Any two mutually orbiting bodies each having non-negligeable mass, such as Mercury and the sun must mutually orbit their common center of mass: while it would be theoretically possible for them to each have perfectly circular orbits, is much more probable for them to have elliptical orbits. An elliptical orbit is necessarily characterized by the body having a constantly changing velocity. This is not to say that a two body system cannot have stable orbits, but just to say that every moment of each orbit sees the velocity become different from the moment before. Yes, this does mean that the sun has a SMALL motion which is its center of mass orbiting the solar system center of mass.
c7ityi: I have work underway on definitively proving a unified field theory is either possible or impossible. It looks very promising so far. Please Register or Log in to view the hidden image! However it does not contain the concept that all particles are small magnets with two poles. :bugeye: Does this mean that all of my work must be burned up now and I must start over? Please Register or Log in to view the hidden image!
jdheiden, I don't think that I agree with you. If a planet is orbiting a star and the speed of its orbit is to slow, it will slowly spiral into the star. As it spirals into the star, its speed may increase but not to the exact amount that is needed to create a stable orbit.
Dale, You honestly don't believe that, do you? If you try to change the speed or direction of a moving object you will experience a force resisting that change. This is the inertial force. If you don't believe me then drop a rock on your foot. You'll feel the force as your foot slows down the rock. This is the same force that is balanced by gravity in order to create a stable orbit.
c7ityi_, I tried to, until you brought it up again. Please Register or Log in to view the hidden image! Just kidding. I couldn't help myself. Actually, magnetic fields are only created by particles that have electric fields. And gravitational mass is also found in neutral particles, so magnetic fields are not required in order to have a gravitational field.
CANGAS, Why not? Why doesn't any small change to a planet's mass or orbital speed cause it to spiral into the Sun or fly off into outer space? Even the smallest change, over billions of years, should create a large effect. And yet, with all the asteroids and comets that hit the Earth, and all of the gravitational fields that pulled at the Earth through its entire life of billions of years, it is still in a stable orbit. That's like dropping a needle and having it land on its tip, and then finding that a hundred years later it's still balanced on its tip.
Ahh, I see the confusion. You are mixing up Newton's 2nd and 3rd laws, it is a very common mixup. The key is to realize that the "reaction" force, what you are calling the inertial force, is acting on a different body than the "action" force. That is why I suggested drawing a free body diagram. You are absolutely correct that if I try to change the speed or direction of a moving (or even stationary) object then I will experience a force. A painful force in the case of the rock example. However, the object will not experience a second force. If you draw the free body diagrams an action-reaction pair always affect different bodies. So, for an orbiting satellite there is only one force acting on it, the gravitational force. The reaction force in this case is an equal-and-opposite gravitational force pulling the earth towards the satellite. There is no balancing force acting on the satellite because the equal-and-opposite forces you are talking about always act on a different free body. Because there is only one force acting on it, the satellite constantly accelerates and constantly travels in a curved path. If there were a balance of forces it would travel in a straight line and not orbit at all. Again, an unbalanced force is required for a stable orbit. -Hope this helps Dale
Prosoothus: What part of the word: "Apparently" is not understandable to you?? What part of the phrase: "in most cases on record" is not understandable to you? And do you so quickly forget my comment regarding: just how much proof DO we have about billions of years of stable orbits?
DaleSpam, There is no confusion. We are only looking at the same condition in two different ways. If I attach a rock to a string and start spinning it, I will feel a force pulling at my hand. This is because the rock wants to go straight, and I'm forcing it to curve. Thanks to the strong muscles in my arm opposing the inertial force of the rock, the rock continues to move in a circular path. Now if I replace the force of my arm with an attractive force, like gravity, that is equal to the inertial force of the rock, the rock will orbit the source of the attractive force just like a planet orbits the Sun.
Beginning with Newton, many of the most prominent physicists have believed that the gravity of the entire universe is responsible for inertia. Science experiments have proved that inertial mass is equal to gravitational mass to an experimental accuracy of one part in one million. This strongly implies that gravitational force IS "inertial force". I personally can consider it only semantics if one says "inertia" or "inertial force".
CANGAS, Well, since life has been developing on Earth for billions of years (that is, if you're not a creationist), and since I'm still alive, I must conclude that the Earth didn't fall into the Sun, or fly into outer space during the last few billion years. Do you have evidence suggesting otherwise?
